Nonlocal mumford-shah regularizers for color image restoration

Miyoun Jung*, Xavier Bresson, Tony F. Chan, Luminita A. Vese

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

104 Scopus citations


We propose here a class of restoration algorithms for color images, based upon the Mumford-Shah (MS) model and nonlocal image information. The Ambrosio-Tortorelli and Shah elliptic approximations are defined to work in a small local neighborhood, which are sufficient to denoise smooth regions with sharp boundaries. However, texture is nonlocal in nature and requires semilocal/non-local information for efficient image denoising and restoration. Inspired from recent works (nonlocal means of Buades, Coll, Morel, and nonlocal total variation of Gilboa, Osher), we extend the local Ambrosio-Tortorelli and Shah approximations to MS functional (MS) to novel nonlocal formulations, for better restoration of fine structures and texture. We present several applications of the proposed nonlocal MS regularizers in image processing such as color image denoising, color image deblurring in the presence of Gaussian or impulse noise, color image inpainting, color image super-resolution, and color filter array demosaicing. In all the applications, the proposed nonlocal regularizers produce superior results over the local ones, especially in image inpainting with large missing regions. We also prove several characterizations of minimizers based upon dual norm formulations.

Original languageEnglish (US)
Article number5635336
Pages (from-to)1583-1598
Number of pages16
JournalIEEE Transactions on Image Processing
Issue number6
StatePublished - Jun 2011
Externally publishedYes


  • Ambrosio-Tortorelli elliptic approximations
  • Mumford-Shah (MS) regularizer
  • deblurring
  • demosaicing
  • denoising
  • impulse noise
  • inpainting
  • nonlocal operators
  • super-resolution

ASJC Scopus subject areas

  • Software
  • Computer Graphics and Computer-Aided Design


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